as the Date/Time fields are stored in epoch time, you cannot just reference a "visible" date format to perform calculations on, you can only use these for an exact Date/Time match.

If you are after determining a calculation for the past 10 days, then you can make use of the $TIMESTAMP$ keyword to give you the current Date/Time and subtract the equivalent 10 days (864000) from this.

Is the 'Last Resolved Date' field a Date only or Date/Time field? This will determine which keyword will work i.e. $DATE$ or $TIMESTAMP$ and also the value to subtract as both these fields are stored differently in the database.

you can drill down which field is causing the issue.. which one is having data mismatch, syntax mismatch or logical relationship error or if the query is syntatically right but it might not find any value from the backend form...